Lie Algebras and Applications
Iachello, Francesco.
Lie Algebras and Applications [electronic resource] / by Francesco Iachello. - XIV, 196 p. 26 illus. online resource. - Lecture Notes in Physics, 708 0075-8450 ; . - Lecture Notes in Physics, 708 .
Basic Concepts -- Semisimple Lie Algebras -- Lie Groups -- Irreducible Bases (Representations) -- Casimir Operators and Their Eigenvalues -- Tensor Operators -- Boson Realizations -- Fermion Realizations -- Differential Realizations -- Matrix Realizations -- Spectrum Generating Algebras and Dynamic Symmetries -- Degeneracy Algebras and Dynamical Algebras.
This book, designed for advanced graduate students and post-graduate researchers, provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, a concise exposition is given of the basic concepts of Lie algebras, their representations and their invariants. The second part contains a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
9783540362395
10.1007/3-540-36239-8 doi
Mathematical physics.
Topological Groups.
Quantum theory.
Mathematical Methods in Physics.
Topological Groups, Lie Groups.
Atomic/Molecular Structure and Spectra.
Particle and Nuclear Physics.
Quantum Physics.
QC5.53
530.15
Lie Algebras and Applications [electronic resource] / by Francesco Iachello. - XIV, 196 p. 26 illus. online resource. - Lecture Notes in Physics, 708 0075-8450 ; . - Lecture Notes in Physics, 708 .
Basic Concepts -- Semisimple Lie Algebras -- Lie Groups -- Irreducible Bases (Representations) -- Casimir Operators and Their Eigenvalues -- Tensor Operators -- Boson Realizations -- Fermion Realizations -- Differential Realizations -- Matrix Realizations -- Spectrum Generating Algebras and Dynamic Symmetries -- Degeneracy Algebras and Dynamical Algebras.
This book, designed for advanced graduate students and post-graduate researchers, provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, a concise exposition is given of the basic concepts of Lie algebras, their representations and their invariants. The second part contains a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
9783540362395
10.1007/3-540-36239-8 doi
Mathematical physics.
Topological Groups.
Quantum theory.
Mathematical Methods in Physics.
Topological Groups, Lie Groups.
Atomic/Molecular Structure and Spectra.
Particle and Nuclear Physics.
Quantum Physics.
QC5.53
530.15